2
a) 81 cm
2
b)90cm
2
c)108cm
2
d)162cm

The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The graph of an inequality is shown below:

What is an inequality equation?

The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.

It's a line with a shaded side on one side to show which xy pairings are the inequality's solutions.

Example -

Let us take an equation, 4x + 8y ≤ -24

Now, solve the above equation in the form of slope-intercept.

4x + 8y ≤ -24

or, 8y ≤ - 4x - 24

or, y ≤ -(1/2)x - 3

Now, the graph becomes according to the slope-intercept form is:

Here we noticed that,

This side of the inequality is shaded below (instead of above) because y is lower than (or equal to) the other side.

Because working with a "or equal to" inequality, draw a solid line rather than a dashed one. Points on the solid line denote locations where the inequality has been solved.

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The x-intercept and y-intercept on the graph will cross the x and y axes accordingly.

In order to find the x-intercept and y-intercept represent in terms of the units on the axes, we must know the definition of each of them.

In math the x-intercept is defined as the value of the x coordinate of a point where the value of y coordinate is equal to zero.

Similarly, the y intercept in math is referred as the point where the graph intersects the y-axis.

While looking into the given definition, we have identified that intercept refer the intersecting point of the graph.

Based on these we have concluded that x and y intercept are the intersecting point of the graph.

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The value of x for the given figure will be equal to √212.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Apply the Pythagorean theorem for the first triangle,

H² = x² - 6²

Apply the Pythagorean theorem for the second triangle,

B² = 27² - x²

Apply the Pythagorean theorem to the third triangle,

H² = 27² - x² - 21²

H² = -x² + 288

x² - 6² = -x² + 288

2x² = 424

x² = 212

x=√212

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The total number of hours driven can be represented by the expression "x + y." This represents the sum of the hours driven in one car (x) and the hours driven in another car (y).

The other expressions do not represent the total number of hours driven. "x y" is not a valid mathematical expression. "y 70" and "300 x" represent the number of miles driven by one car and the number of miles driven by another car, respectively, but do not represent the total number of hours driven. "70x" and "55y" represent the number of miles driven by one car and the number of miles driven by another car, respectively, but do not represent the total number of hours driven.

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You can extrapolate the volume formula to get the missing length of a pyramid with a rectangular base.

Determine the volume of a pyramid with a rectangular base using this formula.

Thus, using your algebraic skills, determine the formula again for missing length of a pyramid with a rectangular base.

L = V / (H x W) / 3.

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333 integers,  there are 333 integers between 1 and 1,000 which are divisible by 3.

The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.

here

add all the numbers,

1 + 2+ 3 + 4+ 5 = 15

and 15/3 = 5

so it is divisible by 3

not by 9

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The triple integration of ∭E xy dV and The Solid Tetrahedron With Vertices (0,0,0),(8,0,0),(0,1,0),(0,0,3), is 8 / 5.

What is integration?

When infinitesimal data are combined, concepts like displacement, area, and volume can be described by assigning numerical values to the functions that make up an integral. Integration is the procedure for locating integrals.

Given:

∭E xy dV  and The Solid Tetrahedron With Vertices (0,0,0),(8,0,0),(0,1,0),(0,0,3),

Calculate the equation of plane passing through the vertices (0,0,0),(8,0,0),(0,1,0),(0,0,3) as shown below,

x / 8 + y / 1 + z / 3 = 1

z = 24 - 3x -24y / 8

Put z = 0

y = 1 - 1 / 8x

Put y = o

x = 8

Calculate the integral as shown below,

[tex]\int \int\int_E xydV = \int _0^8 \int _0^{1-x/8} \int _0^{{24-3x-24y}/8} xy\ dz\ dy\ dx[/tex]

∫∫∫E = [tex]1/8 \int _0^8 [24xy^2 / 2 - 3x^2y^2 / 2 - 24xy^3 / 3]^{1-x /8}dx[/tex]

∫∫∫E = 1 / 8 × 64 / 5

∫∫∫E = 8 / 5

Thus, the triple integral is 8 / 5.

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Answer:

1:3:2

Step-by-step explanation:

Sum of triangle is 180°

A : B : C

30 : 90 : (180 -90 - 30)

30 : 90 : 60

1 : 3 : 2

I hope my answer helps you.

Average number of planes that will stack up waiting to land:  This can vary greatly depending on the size of the airport, the number of flights per day, and the number of runways available.

What is average?

Average, mean, median, and norm all refer to something that sits in the middle. The average is the ratio created by dividing the total number of figures in a set by the total number of figures.

To determine the average number of planes that will stack up waiting to land, we need to know the rate at which planes arrive at the airport and the rate at which they are able to land.

Generally, an airport can expect to experience a queue of up to 10 planes waiting to land at peak times.

Average time a plane must wait in line before it can land: This also varies significantly depending on the airport and the conditions. Generally, a plane must wait an average of 5-7 minutes before it is able to land.

Average time it takes a plane to clear the runway once it has notified the airport that it is in the vicinity and wants to land: This time will depend on the size of the airport, the number of planes in the queue, and the amount of time it takes for the plane to taxi off the runway. Generally, a plane can expect to clear the runway in about 2-3 minutes.

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The fraction simplifies to 1. Option A.

The difference of two squares is a theorem that tells us if a quadratic equation can be written as a product of two binomials, in which one shows the difference of the square roots and the other shows the sum of the square roots, the difference of two squares is a squared (multiplied by itself) number subtracted from another squared number.  This identity is often used in algebra where it is useful in applications to integer factorization, the quadratic sieve, the algebraic factorization, etc.

One thing to note about this theorem is that it does not apply to the SUM of squares.

(32008)²-(32006)²/ (32007)²-(32005)²

(32008 - 32006)² / (32007 - 32005)²

(2)² / (2)²

1

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Applying the triangle midsegment theorem, the length of segment TU = 100 units.

If a line connects the midpoints of two sides of a triangle, it is parallel to the third side, and according to the triangle midsegment theorem, it has a length that is half the measure of the third side of that triangle.

Given the triangle, TUV, where:

Segment TU is a third side to the midsegment HD = 50 units.

Thus, apply the triangle midsegment theorem to find the length of segment TU.

HD = 1/2(TU)

Substitute:

50 = 1/2(TU)

2(50) = TU

100 = TU

TU = 100 units

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Comparing numbers in math is defined as a process or method in which one can determine whether a number is smaller, greater, or equal to another number according to their values.

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Answer:

A=6a2=6×(5)2=6×25=150cm2.

Step-by-step explanation:

After reviewing the generated schedule on Wednesday, you notice your Pharmacy Technician, Abigail Gibson, isn't being scheduled at all during the week. The option that will cause this is B. Availability is not entered

Pharmacy technicians check inventory and fill prescriptions. Pharmacy assistants assist pharmacists in dispensing prescription drugs to patients or medical professionals. Hospitals and retail pharmacies are where they primarily work.

In order to assist and support patients and guarantee they receive the best care, pharmacists collaborate with pharmacy technicians, who are medical professionals.

In addition to primary care, educational, military, or veterinary practices, pharmacy technicians can work in community (retail) pharmacies, hospital pharmacies, pharmaceutical production or sales in the pharmaceutical industry, prisons, and community (retail) pharmacies.

Based on the information illustrated, the correct option is B.

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The value of g(2) = -1/4 and the value of g(-2) = π/2 - 3/2

The graph of function g is having a point of inflection at x=-2 and  x=0 and x = 1 because g''(x) = f'(x) changes at each of these values.

A function is basically a relation between two sets having a domain , range and a co-domain.

We can represent functions graphically by plotting their equations and putting the value of co- ordinates.

A graph consists of four quadrants two positive and two negative. It helps to visualize data in a clear manner and helps to present data more efficiently.

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The terms of expression 4x² - 3xy are

(a) 4x² and -3xy

(b) 4x² and 3xy

(c) 4x² and -xy

(d) x² and xy

A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms. For example, in the expression 4 x + y, the two terms are 4 x and y. It is to be noted here that terms add up to form the expression.

Terms: a2,6a,and 9.

Variables: a2,a

Constants:9

Factors: a,a are the factors of term 1,-6 and a are the factors of term 2,and 9 is the factor of term 3.

Coefficients:1 is the coefficient of a2,-6 is the coefficient of a,and 9 is the coefficient of the constant term

Operators:- and+

Given, the expression is 4x² - 3xy.

We have to find the terms of the expression.

The terms are the numbers or the variables added together.

Each term in an algebraic expression is separated by a + sign or - sign.

Therefore, the terms in the given expression are 4x² and -3xy.

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The slope of 4y =- 4 is zero.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Slope-intercept form:

y = mx+b,

where m is the slope and b is the y-intercept.

Given equation:

4y =- 4

To find the slope:

First, we simplify the equation.

Divide by 4.

(4/4)y = -4/4

y = -1

Now, we know the slope-intercept form:

y = mx+b,

where m is the slope and b is the y-intercept.

Comparing, both the equation,

we get,

m = 0.

So, the slope is 0.

Therefore, the slope is 0. This produces a horizontal line.

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In the triangle LMN, the angle opposite side LM is indicated by the supplied figure as being ∠N.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint.

The Latin word "angulus," which means "corner," is the source of the English term "angle."

The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.

So, according to the given figure, the angle opposite to side LM in triangle LMN is ∠n.

Therefore, in the triangle LMN, the angle opposite side LM is indicated by the supplied figure as being ∠N.

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Answer:9/5

Step-by-step explanation:

Answer:

A. 9/5

C. 1 4/5

Step-by-step explanation:

3 x 3/5 = (3 x 3)/5 = 9/5

9/5 = 5/5 + 4/5 = 1 4/5

As per the distance formula, the longest side of triangle ABC is AB and the difference point is 9.1 units.

The formula to calculate the distance of two coordinates is written as

=> d = √(x2 - x1)² + (y2 - y1)²

where (x1, y1) and (x2, y2) are the coordinates.

Here we have given that ∆ABC has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices.

And we need to find the measure of the longest side of ∆ABC is units.

Here we have to take the points A and B and then we need to find the distance for the points AB,

AB = √(-2 - 7)² + (2 - 1)²

AB = √(-9)² + (1)²

AB = √81 + 1

AB = √82 = 9.1

Now, we have to take the next two points, and then we have to find the distance between the points,

BC = √(4 - (-2))² + (2 - 2)²

BC = √(6)² + (0)²

BC = √36 + 0

BC = √36 = 6

Finally, we have to calculate the distance between the point C and A then we get,

CA = √(7 - 4)² + (1 - 2)²

CA = √(3)² + (-1)²

CA = √9 + 1

CA = √10 = 3.2

While looking into the given distance we have identified the the point AB has the longest side.

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The formula for determining a z-score is z = (x-μ)/σ, where x is the raw score, z is the population mean, and z is the population standard deviation.

X=(z)(SD) + mean

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There are three types of discontinuity.

If a function f(x) is not continuous at a point 'a' in its domain D, it is said to be discontinuous at that location. A point of discontinuity of the function is thus referred to as point "a."

Any of the following scenarios might cause the discontinuity:

Discontinuity of the First Type: If the right hand of the function exists but is not equal to f, then the function f(x) is said to have a discontinuity of the first kind from the right at x = a. (a). The Left-Hand Limit and the Right-Hand Limit both exist in Jump Discontinuity and are finite, but they are not equivalent to one another.

Discontinuity of the Second Type: If a function f(x) at x = a has neither a left-hand limit nor a right-hand limit, it is said to have discontinuity of the second kind.

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Discontinuity of the First Type: If the right hand of the function exists but is not equal to f, then the function f(x) is said to have a discontinuity of the first kind from the right at x = a. (a). The Left-Hand Limit and the Right-Hand Limit both exist in Jump Discontinuity and are finite, but they are not equivalent to one another.

The trick for table 13 are as follows.

A multiplication chart is a table that displays the products of two numbers.  One set of numbers is typically written in the left column, while another set is written in the top row. The numbers in the products are listed in a rectangular array. Addition is repeated when you multiply.

To learn table fast follow points,

1. To learn the 13 times table, we must first learn the 3 times table. 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30 are the multiples of 3.

2. Add natural numbers to the tenth digit of the multiples of 3 to get the multiples of 13. As a result, the 13 times table can be derived as follows: 1+0)3, (2+0)6, (3+0)9, (4+1)2, (5+1)5, (6+1)8, (7+2)1, (8+2)4, (9+2)7, (10+3)0 = 13, 26, 39, 52, 65, 78, 91, 104, 117, 130.

3. The 13 multiplication table does not have any rules that make it easy to remember, but there is a pattern for every ten multiples of three: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130. Students can remember these digits to help them with the 13 times table because the last digit of these multiples always repeats.

Hence, follow the steps to learn table of 13.

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Right triangles ABC and DEF are drawn to measure the slope of the line is:

a) run = 2 rise = 3 slope = 3/2

b) run = 6 rise = 9 slope = 9/6 = 3/2

c) Yes, they are similar because the 2 triangles are similar.

Two triangles are similar if they meet one of the following criteria. : Two pairs of corresponding angles are equal.

What is Right triangles?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

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Answer:

B

Step-by-step explanation:

A = 0.5kg (Not close)

B = 0.05

C = 0.02 ( Not close)

D = 0.04

(Explanation why answer is B and not D)

B is closet because even we round off to two decimal places 0.05kg answer comes not 0.04kg

Plus 0.05 is 0.01kg away from 0.049, While 0.04kg is 0.09kg away from 0.049kg.

I hope my answer helps you.

1/20 kg is closest to 0.049 kg among the given choices. So, correct option is B.

To determine which option is closest to 0.049 kg, we can compare the given options to the target value and find the option with the smallest absolute difference.

A. ½ kg = 0.5 kg (Difference = |0.5 kg - 0.049 kg| ≈ 0.451 kg)

B. 1/20 kg = 0.05 kg (Difference = |0.05 kg - 0.049 kg| = 0.001 kg)

C. 1/50 kg = 0.02 kg (Difference = |0.02 kg - 0.049 kg| ≈ 0.029 kg)

D. 2/50 kg = 0.04 kg (Difference = |0.04 kg - 0.049 kg| = 0.009 kg)

Comparing the absolute differences, we can see that option B (1/20 kg = 0.05 kg) has the smallest difference from 0.049 kg, which is only 0.001 kg.

Therefore, option B (1/20 kg) is closest to 0.049 kg among the given choices.

When dealing with questions like this, it is helpful to compare the values using the absolute difference from the target value. The option with the smallest absolute difference is the closest approximation to the target value. In this case, 1/20 kg provides the closest value to 0.049 kg, making it the correct choice.

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Answer:

In astronomy, the celestial equator is the great circle in which the plane of the terrestrial Equator intersects the celestial sphere; it consequently is equidistant from the celestial poles. When the Sun lies in its plane, day and night are everywhere of equal length, a twice-per-year occurrence known as equinox.

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Step-by-step explanation:

By using multiplication and subtraction, it can be calculated that-

Austin has to pay $9 for 3 pounds of chicken

Austin has to pay $(10.50 [tex]\times[/tex] p- 1.50)  for p pounds of chicken

What is subtraction and multiplication?
To find how big or small one number is from the other, then the operation used is called subtraction of numbers

Repeated addition is called multiplication. Multiplication is used to find the product of two or more numbers

Here, subtraction and multiplication is used

Cost of one pound of chicken = $3.50

Cost of three pounds of chicken = $3.50 [tex]\times[/tex] 3 = $10.50

He has a coupon for $1.50 off the final amount.

Amount of money Austin has to pay for 3 pounds of chicken =

$(10.50 - 1.50) = $9

Amount of money Austin has to pay for p pounds of chicken =

$(10.50 [tex]\times[/tex] p- 1.50)

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Answer:

One of them must be a mirror image of the other

Step-by-step explanation:

Two shapes are congruent if one is a mirror shape of the other or if both have the same size.

The domain of a function as described by the question, can be found by solving a given function for x such that the values of  x satisfy the equation. And the vertical asymptotes  can be found by solving for x values which make the equation go towards positive or negative infinity.

A straight line that continuously approaches a certain curve without ever meeting it is an asymptote. To put it another way, an asymptote is a line that a curve travels towards as it approaches infinity.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f(x) make up this set x.

As asked by the question, the domain of a function can be found by solving the equation f(x) = y for values of x such that the values of x give out a single value y. Similarly, the vertical asymptotes can be found from a rational function [tex]\frac{p(x)}{q(x)}[/tex] by equating the denominator q(x) to 0 and solving for x.  i.e q(x) = 0.

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The profit per month for the contractor is obtained as $9425.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

The profit of the contractor per job is given as $3250.

As per the given table the expected value can be obtained as,

E(x) = [tex]\sum_{x = 1}^{4} xP(x)[/tex]

⇒ E(x) = 1 × 0.1 + 2 × 0.2 + 3 × 0.4 + 4 × 0.3

⇒ 2.9

Then, the expected profit of is given as 3250 × 2.9 = $9425

Hence, the profit per month is obtained as $9425.

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